Is it permissible to continue exercising to maintain health and vitality, or should one abandon it for fear of self-admiration, especially given that the body responds to even the slightest amount of exercise?

Arrogance (ʿujb) is to consider a blessing great and to rely on it, while forgetting to attribute it to the Bestower. It has three states: 1. Fear of the blessing disappearing or being taken away, and this is not arrogance. 2. Rejoicing in the blessing because it is from Allah the Almighty, and this is not arrogance. 3. Rejoicing in the blessing and feeling secure in it because it is considered an inherent quality and attributed to oneself, not to Allah the Almighty, and this is arrogance.

What you feel is not arrogance, because you realize that the blessings you have been granted are from Allah’s grace upon you. Your abandoning exercises for fear of falling into arrogance is proof that you are free from arrogance. Therefore, you should not abandon exercises that are beneficial for your health.